Description of fast matrix multiplication algorithm: ⟨7×8×9:347⟩

Algorithm type

8 X^{4} Y^{4} Z^{4} + 8 X^{4} Y^{4} Z^{3} + 16 X^{2} Y^{6} Z^{2} + 8 X^{2} Y^{2} Z^{5} + 16 X^{2} Y^{2} Z^{4} + X^{3} Y Z^{3} + 28 X^{2} Y^{2} Z^{3} + 9 X Y^{3} Z^{3} + X Y Z^{5} + 3 X^{3} Y Z^{2} + 45 X^{2} Y^{2} Z^{2} + X^{2} Y Z^{3} + 10 X Y^{3} Z^{2} + 6 X Y^{2} Z^{3} + X Y Z^{4} + 2 X^{3} Y Z + 14 X^{2} Y^{2} Z + 5 X^{2} Y Z^{2} + 23 X Y^{3} Z + 5 X Y^{2} Z^{2} + 41 X Y Z^{3} + 7 X^{2} Y Z + 2 X Y^{2} Z + 49 X Y Z^{2} + 38 X Y Z

Algorithm definition

The algorithm ⟨7×8×9:347⟩ is taken from:

Andrew I. Perminov. FastMatrixMultiplication, GitHub, February 2026. [ GitHub repository ]

Algorithm description

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.

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